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Block #652,770

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/29/2014, 2:31:58 AM Β· Difficulty 10.9546 Β· 6,153,574 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
d7562882173ff4b3003cac1a6b91800265272bf352fe3c6e74ded268f7b1854e
View on Chainz β†—

Height

#652,770

Difficulty

10.954610

Transactions

2

Size

728 B

Version

2

Bits

0af4615a

Nonce

1,399,681,852

Timestamp

7/29/2014, 2:31:58 AM

Confirmations

6,153,574

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a5854cf14c7d1d3d394d8829e8b594982671d63cb42c0855478d1b6fab959fd0
Transactions (2)
Coinbasebe8a3032bda5f2…208f8ce60492c5
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
03ac9cce87a8ec…b46ced4ff3f7c9
3 in β†’ 2 out10.3211 XPM521 B
AH8QkSBM…W2xh1GcYAVYi1Ne3…o5MBMUSM
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.355 Γ— 10⁹⁸(99-digit number)
13558116688842434276…45047046761239933439
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.355 Γ— 10⁹⁸(99-digit number)
13558116688842434276…45047046761239933439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.355 Γ— 10⁹⁸(99-digit number)
13558116688842434276…45047046761239933441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.711 Γ— 10⁹⁸(99-digit number)
27116233377684868552…90094093522479866879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.711 Γ— 10⁹⁸(99-digit number)
27116233377684868552…90094093522479866881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.423 Γ— 10⁹⁸(99-digit number)
54232466755369737104…80188187044959733759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.423 Γ— 10⁹⁸(99-digit number)
54232466755369737104…80188187044959733761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁹(100-digit number)
10846493351073947420…60376374089919467519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.084 Γ— 10⁹⁹(100-digit number)
10846493351073947420…60376374089919467521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.169 Γ— 10⁹⁹(100-digit number)
21692986702147894841…20752748179838935039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.169 Γ— 10⁹⁹(100-digit number)
21692986702147894841…20752748179838935041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.338 Γ— 10⁹⁹(100-digit number)
43385973404295789683…41505496359677870079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,694,837 XPMΒ·at block #6,806,343 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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