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Block #418,847

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/25/2014, 4:59:40 AM Β· Difficulty 10.3830 Β· 6,385,234 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a0a6ca9946f2b146b13f621d68b3bc49511c330fa9f840583d6d02e5af3ecf3f
View on Chainz β†—

Height

#418,847

Difficulty

10.382954

Transactions

3

Size

650 B

Version

2

Bits

0a620949

Nonce

3,179,773

Timestamp

2/25/2014, 4:59:40 AM

Confirmations

6,385,234

Mined by

⛏️ P2SHAXUw4uV3VsR6XC6PcJYfCBEa6abd6wJj6h

Merkle Root

4ee6a88db6d5b1bcd1a001c950c3ee414683acb016975eed74bb1e781835c0cd
Transactions (3)
Coinbase183876df1bb929…6e763040a9e2df
1 in β†’ 1 out9.2800 XPM109 B
AXUw4uV3…bd6wJj6h
ed3972eacf6564…d3803700906725
1 in β†’ 2 out4.0176 XPM226 B
AQfdq4WM…wbGrV8QPATiV5dCK…q2jDT9yR
578cfa499632c3…cb476339c327d9
1 in β†’ 2 out3.0756 XPM225 B
Ac4fDFQL…VD4NTHBPAKXhPPA8…TAM82Pjk
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.

3.954 Γ— 10⁹⁴(95-digit number)
39548597713303722235…39936325418188134739
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
3.954 Γ— 10⁹⁴(95-digit number)
39548597713303722235…39936325418188134739
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.954 Γ— 10⁹⁴(95-digit number)
39548597713303722235…39936325418188134741
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
7.909 Γ— 10⁹⁴(95-digit number)
79097195426607444470…79872650836376269479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.909 Γ— 10⁹⁴(95-digit number)
79097195426607444470…79872650836376269481
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
1.581 Γ— 10⁹⁡(96-digit number)
15819439085321488894…59745301672752538959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.581 Γ— 10⁹⁡(96-digit number)
15819439085321488894…59745301672752538961
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
3.163 Γ— 10⁹⁡(96-digit number)
31638878170642977788…19490603345505077919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.163 Γ— 10⁹⁡(96-digit number)
31638878170642977788…19490603345505077921
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
6.327 Γ— 10⁹⁡(96-digit number)
63277756341285955576…38981206691010155839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.327 Γ— 10⁹⁡(96-digit number)
63277756341285955576…38981206691010155841
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:57,676,697 XPMΒ·at block #6,804,080 Β· updates every 60s
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