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Block #1,346,391

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2015, 8:56:23 PM Β· Difficulty 10.8219 Β· 5,480,456 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fdc052a69839f0a74c69cd6e11c457e574f2a3eb37e7ef0325ac5ef5ab50cb3c
View on Chainz β†—

Height

#1,346,391

Difficulty

10.821910

Transactions

1

Size

200 B

Version

2

Bits

0ad268b5

Nonce

137,730,508

Timestamp

11/28/2015, 8:56:23 PM

Confirmations

5,480,456

Mined by

⛏️ P2SHAYo5es1Q5qkBNTBRZLFtfNAqfp9JYywSps

Merkle Root

da03f2cc013174d393039c9cfb3782865317999213d41d4e15e58e47d35c20f2
Transactions (1)
Coinbaseda03f2cc013174…e58e47d35c20f2
1 in β†’ 1 out8.5300 XPM109 B
AYo5es1Q…9JYywSps
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.

1.493 Γ— 10⁹⁷(98-digit number)
14932167687207470309…11189651394617343999
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
1.493 Γ— 10⁹⁷(98-digit number)
14932167687207470309…11189651394617343999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.493 Γ— 10⁹⁷(98-digit number)
14932167687207470309…11189651394617344001
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
2.986 Γ— 10⁹⁷(98-digit number)
29864335374414940619…22379302789234687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.986 Γ— 10⁹⁷(98-digit number)
29864335374414940619…22379302789234688001
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
5.972 Γ— 10⁹⁷(98-digit number)
59728670748829881239…44758605578469375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.972 Γ— 10⁹⁷(98-digit number)
59728670748829881239…44758605578469376001
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
1.194 Γ— 10⁹⁸(99-digit number)
11945734149765976247…89517211156938751999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.194 Γ— 10⁹⁸(99-digit number)
11945734149765976247…89517211156938752001
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
2.389 Γ— 10⁹⁸(99-digit number)
23891468299531952495…79034422313877503999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.389 Γ— 10⁹⁸(99-digit number)
23891468299531952495…79034422313877504001
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:57,858,942 XPMΒ·at block #6,826,846 Β· updates every 60s
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