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Block #1,391,635

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/30/2015, 2:09:32 PM Β· Difficulty 10.8081 Β· 5,450,155 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
933363a4984494d8b46b13d6a0af1037d42a18de7afc1a8a6b5f1ec8e1fdd27c
View on Chainz β†—

Height

#1,391,635

Difficulty

10.808094

Transactions

2

Size

1.14 KB

Version

2

Bits

0acedf42

Nonce

512,310,801

Timestamp

12/30/2015, 2:09:32 PM

Confirmations

5,450,155

Mined by

⛏️ P2SHAQV2Ef51Gg24fuqua1XXLFMcSWwDGfbnqT

Merkle Root

f01c8007c94f4548c85873b8ec3283cdadfa5d6747b684e858b198241d68eb59
Transactions (2)
Coinbasec85c3a41727079…ca4a06fe72338f
1 in β†’ 1 out8.5700 XPM110 B
AQV2Ef51…wDGfbnqT
8f8195351bfb97…d3ce5e2eaf4fbd
6 in β†’ 2 out14.0100 XPM965 B
ASE76mJE…gk3DscCMAGky5ni4…jnaoQ88P
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.

3.190 Γ— 10⁹⁢(97-digit number)
31902103385832401086…88203611281766653439
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
3.190 Γ— 10⁹⁢(97-digit number)
31902103385832401086…88203611281766653439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.190 Γ— 10⁹⁢(97-digit number)
31902103385832401086…88203611281766653441
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
6.380 Γ— 10⁹⁢(97-digit number)
63804206771664802173…76407222563533306879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.380 Γ— 10⁹⁢(97-digit number)
63804206771664802173…76407222563533306881
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
1.276 Γ— 10⁹⁷(98-digit number)
12760841354332960434…52814445127066613759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.276 Γ— 10⁹⁷(98-digit number)
12760841354332960434…52814445127066613761
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
2.552 Γ— 10⁹⁷(98-digit number)
25521682708665920869…05628890254133227519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.552 Γ— 10⁹⁷(98-digit number)
25521682708665920869…05628890254133227521
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
5.104 Γ— 10⁹⁷(98-digit number)
51043365417331841738…11257780508266455039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.104 Γ— 10⁹⁷(98-digit number)
51043365417331841738…11257780508266455041
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:57,978,698 XPMΒ·at block #6,841,789 Β· updates every 60s
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