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Block #470,876

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/2/2014, 5:42:52 AM Β· Difficulty 10.4289 Β· 6,323,517 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38f12f034477b238032a145474f36d1c414eeec549a44955e03b3e81cece61fe
View on Chainz β†—

Height

#470,876

Difficulty

10.428872

Transactions

1

Size

199 B

Version

2

Bits

0a6dca89

Nonce

2,800,224

Timestamp

4/2/2014, 5:42:52 AM

Confirmations

6,323,517

Mined by

⛏️ P2SHAUr2mi9NVbZVyVe7ntgXEyremKUbNcUCGh

Merkle Root

36e21bafb27dcb7b1d9b0795797ff5a3e7cb0951813d1d228c9fc42983ee73fe
Transactions (1)
Coinbase36e21bafb27dcb…9fc42983ee73fe
1 in β†’ 1 out9.1800 XPM109 B
AUr2mi9N…UbNcUCGh
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.

1.481 Γ— 10⁹⁴(95-digit number)
14815456106047271966…31295383786424718549
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
1.481 Γ— 10⁹⁴(95-digit number)
14815456106047271966…31295383786424718549
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.481 Γ— 10⁹⁴(95-digit number)
14815456106047271966…31295383786424718551
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
2.963 Γ— 10⁹⁴(95-digit number)
29630912212094543933…62590767572849437099
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.963 Γ— 10⁹⁴(95-digit number)
29630912212094543933…62590767572849437101
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
5.926 Γ— 10⁹⁴(95-digit number)
59261824424189087867…25181535145698874199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.926 Γ— 10⁹⁴(95-digit number)
59261824424189087867…25181535145698874201
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
1.185 Γ— 10⁹⁡(96-digit number)
11852364884837817573…50363070291397748399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.185 Γ— 10⁹⁡(96-digit number)
11852364884837817573…50363070291397748401
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
2.370 Γ— 10⁹⁡(96-digit number)
23704729769675635147…00726140582795496799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.370 Γ— 10⁹⁡(96-digit number)
23704729769675635147…00726140582795496801
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:57,599,174 XPMΒ·at block #6,794,392 Β· updates every 60s
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