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Block #1,429,101

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/26/2016, 4:01:34 PM Β· Difficulty 10.7416 Β· 5,414,746 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64d9c7f8317e1931f10e304bff76063f0a2c9ca8e6cf55b5f007d4a58ffa4069
View on Chainz β†—

Height

#1,429,101

Difficulty

10.741625

Transactions

1

Size

201 B

Version

2

Bits

0abddb1c

Nonce

1,943,386,488

Timestamp

1/26/2016, 4:01:34 PM

Confirmations

5,414,746

Mined by

⛏️ P2SHAVdsrzZpvghWxaHUvFUnTEe2rtjRHd8XjJ

Merkle Root

6c3ef9677f57d6fac5d61a69a6fe6c3eeaf44f1bec11d12bb20a98cffc41a0f6
Transactions (1)
Coinbase6c3ef9677f57d6…0a98cffc41a0f6
1 in β†’ 1 out8.6500 XPM110 B
AVdsrzZp…jRHd8XjJ
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.

1.551 Γ— 10⁹⁢(97-digit number)
15518710070483694356…58996401779096442879
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
1.551 Γ— 10⁹⁢(97-digit number)
15518710070483694356…58996401779096442879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.551 Γ— 10⁹⁢(97-digit number)
15518710070483694356…58996401779096442881
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
3.103 Γ— 10⁹⁢(97-digit number)
31037420140967388712…17992803558192885759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.103 Γ— 10⁹⁢(97-digit number)
31037420140967388712…17992803558192885761
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
6.207 Γ— 10⁹⁢(97-digit number)
62074840281934777424…35985607116385771519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.207 Γ— 10⁹⁢(97-digit number)
62074840281934777424…35985607116385771521
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
1.241 Γ— 10⁹⁷(98-digit number)
12414968056386955484…71971214232771543039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.241 Γ— 10⁹⁷(98-digit number)
12414968056386955484…71971214232771543041
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
2.482 Γ— 10⁹⁷(98-digit number)
24829936112773910969…43942428465543086079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.482 Γ— 10⁹⁷(98-digit number)
24829936112773910969…43942428465543086081
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:57,995,142 XPMΒ·at block #6,843,846 Β· updates every 60s
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