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Block #375,656

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/25/2014, 8:57:47 PM Β· Difficulty 10.4242 Β· 6,469,705 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c7c7c0901adef0b8fb15e67ac949ff1bb7c43987213b3d41836434ee5f78787d
View on Chainz β†—

Height

#375,656

Difficulty

10.424166

Transactions

1

Size

207 B

Version

2

Bits

0a6c9629

Nonce

17,901

Timestamp

1/25/2014, 8:57:47 PM

Confirmations

6,469,705

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a40037f126721c0143c243eb671907be4427f8b09735ebe2105aca596ad7dd50
Transactions (1)
Coinbasea40037f126721c…5aca596ad7dd50
1 in β†’ 1 out9.1900 XPM116 B
AbwWkWZt…kawDhufa
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.

6.825 Γ— 10⁹⁷(98-digit number)
68251841862223311384…55652371168319656159
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
6.825 Γ— 10⁹⁷(98-digit number)
68251841862223311384…55652371168319656159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.825 Γ— 10⁹⁷(98-digit number)
68251841862223311384…55652371168319656161
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
1.365 Γ— 10⁹⁸(99-digit number)
13650368372444662276…11304742336639312319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.365 Γ— 10⁹⁸(99-digit number)
13650368372444662276…11304742336639312321
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
2.730 Γ— 10⁹⁸(99-digit number)
27300736744889324553…22609484673278624639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.730 Γ— 10⁹⁸(99-digit number)
27300736744889324553…22609484673278624641
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
5.460 Γ— 10⁹⁸(99-digit number)
54601473489778649107…45218969346557249279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.460 Γ— 10⁹⁸(99-digit number)
54601473489778649107…45218969346557249281
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
1.092 Γ— 10⁹⁹(100-digit number)
10920294697955729821…90437938693114498559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.092 Γ— 10⁹⁹(100-digit number)
10920294697955729821…90437938693114498561
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:58,007,332 XPMΒ·at block #6,845,360 Β· updates every 60s
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