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Block #632,422

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2014, 5:05:03 AM Β· Difficulty 10.9629 Β· 6,181,540 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f06bb3ffee4e200e1017da8d62046b98769f179275ea0f731be6ba020b99a351
View on Chainz β†—

Height

#632,422

Difficulty

10.962937

Transactions

2

Size

400 B

Version

2

Bits

0af68307

Nonce

557,284,109

Timestamp

7/14/2014, 5:05:03 AM

Confirmations

6,181,540

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7c6bd4b677088443b4e3bdad95665c3e04190e46e03acd2b15912abc7922e09a
Transactions (2)
Coinbaseae483c086350b1…71364f2d469a3e
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
ef88b9462d750c…0ae46260dc9f7a
1 in β†’ 2 out8.3000 XPM192 B
AGLZ8STd…6UQvoEJwAeKNrjNj…1NEq95Ta
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.

2.549 Γ— 10⁹⁸(99-digit number)
25498216826707923163…13733798708862484479
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
2.549 Γ— 10⁹⁸(99-digit number)
25498216826707923163…13733798708862484479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.549 Γ— 10⁹⁸(99-digit number)
25498216826707923163…13733798708862484481
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
5.099 Γ— 10⁹⁸(99-digit number)
50996433653415846327…27467597417724968959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.099 Γ— 10⁹⁸(99-digit number)
50996433653415846327…27467597417724968961
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
1.019 Γ— 10⁹⁹(100-digit number)
10199286730683169265…54935194835449937919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.019 Γ— 10⁹⁹(100-digit number)
10199286730683169265…54935194835449937921
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
2.039 Γ— 10⁹⁹(100-digit number)
20398573461366338530…09870389670899875839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.039 Γ— 10⁹⁹(100-digit number)
20398573461366338530…09870389670899875841
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
4.079 Γ— 10⁹⁹(100-digit number)
40797146922732677061…19740779341799751679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.079 Γ— 10⁹⁹(100-digit number)
40797146922732677061…19740779341799751681
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
8.159 Γ— 10⁹⁹(100-digit number)
81594293845465354123…39481558683599503359
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:57,755,773 XPMΒ·at block #6,813,961 Β· updates every 60s
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