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Block #455,046

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/22/2014, 8:16:10 AM Β· Difficulty 10.4020 Β· 6,341,015 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ef1a23976cfffc45612c5e7f7df1578764a91ae10c59aaa8400a9e98e6938b17
View on Chainz β†—

Height

#455,046

Difficulty

10.401994

Transactions

1

Size

208 B

Version

2

Bits

0a66e910

Nonce

39,312

Timestamp

3/22/2014, 8:16:10 AM

Confirmations

6,341,015

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

64328dd71547618472fb2b4377c9b7a9c616f7ac4fac7a97656352a8b7fd3e7b
Transactions (1)
Coinbase64328dd7154761…6352a8b7fd3e7b
1 in β†’ 1 out9.2300 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.

2.471 Γ— 10⁹⁸(99-digit number)
24714579397415666617…77781015708287968279
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
2.471 Γ— 10⁹⁸(99-digit number)
24714579397415666617…77781015708287968279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.471 Γ— 10⁹⁸(99-digit number)
24714579397415666617…77781015708287968281
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
4.942 Γ— 10⁹⁸(99-digit number)
49429158794831333235…55562031416575936559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.942 Γ— 10⁹⁸(99-digit number)
49429158794831333235…55562031416575936561
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
9.885 Γ— 10⁹⁸(99-digit number)
98858317589662666470…11124062833151873119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.885 Γ— 10⁹⁸(99-digit number)
98858317589662666470…11124062833151873121
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
1.977 Γ— 10⁹⁹(100-digit number)
19771663517932533294…22248125666303746239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.977 Γ— 10⁹⁹(100-digit number)
19771663517932533294…22248125666303746241
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
3.954 Γ— 10⁹⁹(100-digit number)
39543327035865066588…44496251332607492479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.954 Γ— 10⁹⁹(100-digit number)
39543327035865066588…44496251332607492481
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:57,612,584 XPMΒ·at block #6,796,060 Β· updates every 60s
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