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Block #417,983

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/24/2014, 12:54:38 PM Β· Difficulty 10.3950 Β· 6,398,879 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
851edae74e48049fa0fc9805b32fdaeece387059d2280be30bee4ddaa74f4790
View on Chainz β†—

Height

#417,983

Difficulty

10.395047

Transactions

2

Size

390 B

Version

2

Bits

0a6521cf

Nonce

128,659

Timestamp

2/24/2014, 12:54:38 PM

Confirmations

6,398,879

Mined by

⛏️ P2SHAd2HQJQEfs21g8HbVK59rCveSTQR3D79qS

Merkle Root

779214dac192a78143407fe10271e7ba4653e4c320834e0a6038ad9e916a31e7
Transactions (2)
Coinbase5f8e1820c52624…22a4aef7ad8521
1 in β†’ 1 out9.2500 XPM109 B
Ad2HQJQE…QR3D79qS
f24154e5eb2315…30a673a03ed228
1 in β†’ 1 out1.4565 XPM192 B
AN6Gx9Bz…dtnYoAEw
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.

1.929 Γ— 10⁹³(94-digit number)
19296324201505025125…53910836944311521879
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
1.929 Γ— 10⁹³(94-digit number)
19296324201505025125…53910836944311521879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.929 Γ— 10⁹³(94-digit number)
19296324201505025125…53910836944311521881
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
3.859 Γ— 10⁹³(94-digit number)
38592648403010050251…07821673888623043759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.859 Γ— 10⁹³(94-digit number)
38592648403010050251…07821673888623043761
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
7.718 Γ— 10⁹³(94-digit number)
77185296806020100503…15643347777246087519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.718 Γ— 10⁹³(94-digit number)
77185296806020100503…15643347777246087521
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
1.543 Γ— 10⁹⁴(95-digit number)
15437059361204020100…31286695554492175039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.543 Γ— 10⁹⁴(95-digit number)
15437059361204020100…31286695554492175041
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
3.087 Γ— 10⁹⁴(95-digit number)
30874118722408040201…62573391108984350079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.087 Γ— 10⁹⁴(95-digit number)
30874118722408040201…62573391108984350081
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
6.174 Γ— 10⁹⁴(95-digit number)
61748237444816080403…25146782217968700159
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:57,778,940 XPMΒ·at block #6,816,861 Β· updates every 60s
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