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Block #462,625

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/27/2014, 1:34:33 PM Β· Difficulty 10.4150 Β· 6,364,215 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
80e35c48a68cacd660e61bfa886f6a2e5f82413399efc6423c0acfbe0b9bd2c1
View on Chainz β†—

Height

#462,625

Difficulty

10.415035

Transactions

2

Size

721 B

Version

2

Bits

0a6a3fbe

Nonce

12,239,295

Timestamp

3/27/2014, 1:34:33 PM

Confirmations

6,364,215

Mined by

⛏️ P2SHAVZ2HmJYxdghJKD7J1pPMxVv1ncMt5YEPK

Merkle Root

55661180c95b7ca3378ad5e7274530de0587538f3a3fe8fd96b8851d27a0ab80
Transactions (2)
Coinbase45622273d43c27…36abe1a1d7245a
1 in β†’ 1 out9.2100 XPM109 B
AVZ2HmJY…cMt5YEPK
f119dd9ba23d63…bd11cb4d03816e
3 in β†’ 2 out19.9384 XPM521 B
AMSj35t4…12GtKPQAAd2wCp2E…2K7cGjX5
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.

1.178 Γ— 10⁹⁢(97-digit number)
11788129584830256823…31605944144691530239
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
1.178 Γ— 10⁹⁢(97-digit number)
11788129584830256823…31605944144691530239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.178 Γ— 10⁹⁢(97-digit number)
11788129584830256823…31605944144691530241
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
2.357 Γ— 10⁹⁢(97-digit number)
23576259169660513647…63211888289383060479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.357 Γ— 10⁹⁢(97-digit number)
23576259169660513647…63211888289383060481
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
4.715 Γ— 10⁹⁢(97-digit number)
47152518339321027295…26423776578766120959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.715 Γ— 10⁹⁢(97-digit number)
47152518339321027295…26423776578766120961
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
9.430 Γ— 10⁹⁢(97-digit number)
94305036678642054590…52847553157532241919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.430 Γ— 10⁹⁢(97-digit number)
94305036678642054590…52847553157532241921
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
1.886 Γ— 10⁹⁷(98-digit number)
18861007335728410918…05695106315064483839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.886 Γ— 10⁹⁷(98-digit number)
18861007335728410918…05695106315064483841
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:57,858,887 XPMΒ·at block #6,826,839 Β· updates every 60s
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