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Block #652,342

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/28/2014, 7:46:43 PM Β· Difficulty 10.9544 Β· 6,155,544 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ef89e34bfa534ab1340bac7626712c2818a972bf44b008d6d9c1496faba2920
View on Chainz β†—

Height

#652,342

Difficulty

10.954390

Transactions

2

Size

2.85 KB

Version

2

Bits

0af452e0

Nonce

1,217,302,949

Timestamp

7/28/2014, 7:46:43 PM

Confirmations

6,155,544

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

af72c9b11a2ddedcc4f4648074da588f9136ac2e09db112ebf9bf00b9e4fa734
Transactions (2)
Coinbase167419c39c7ff6…5b0a00d7c63b85
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
bf45c64df6ed76…5928360204e02d
18 in β†’ 1 out38.3291 XPM2.65 KB
AUfFUyLC…Yn2PxLEq
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.

1.173 Γ— 10⁹⁸(99-digit number)
11736718075917518562…85952696554427187199
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
1.173 Γ— 10⁹⁸(99-digit number)
11736718075917518562…85952696554427187199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.173 Γ— 10⁹⁸(99-digit number)
11736718075917518562…85952696554427187201
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
2.347 Γ— 10⁹⁸(99-digit number)
23473436151835037125…71905393108854374399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.347 Γ— 10⁹⁸(99-digit number)
23473436151835037125…71905393108854374401
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
4.694 Γ— 10⁹⁸(99-digit number)
46946872303670074251…43810786217708748799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.694 Γ— 10⁹⁸(99-digit number)
46946872303670074251…43810786217708748801
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
9.389 Γ— 10⁹⁸(99-digit number)
93893744607340148502…87621572435417497599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.389 Γ— 10⁹⁸(99-digit number)
93893744607340148502…87621572435417497601
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
1.877 Γ— 10⁹⁹(100-digit number)
18778748921468029700…75243144870834995199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.877 Γ— 10⁹⁹(100-digit number)
18778748921468029700…75243144870834995201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,707,123 XPMΒ·at block #6,807,885 Β· updates every 60s
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