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Block #645,027

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2014, 6:04:19 PM Β· Difficulty 10.9541 Β· 6,165,955 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3101f253240d1a3516cffa938112e0cacdb04bea8d04b33d208f33a06f231bb
View on Chainz β†—

Height

#645,027

Difficulty

10.954055

Transactions

1

Size

207 B

Version

2

Bits

0af43cf8

Nonce

2,517,716,397

Timestamp

7/23/2014, 6:04:19 PM

Confirmations

6,165,955

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c7527c3ee06864116abcb82c94deb203f5825c4e892ef7abaacc04844ffc01c2
Transactions (1)
Coinbasec7527c3ee06864…cc04844ffc01c2
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.483 Γ— 10⁹⁢(97-digit number)
34832641381549014430…15943836077469582239
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
3.483 Γ— 10⁹⁢(97-digit number)
34832641381549014430…15943836077469582239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.483 Γ— 10⁹⁢(97-digit number)
34832641381549014430…15943836077469582241
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
6.966 Γ— 10⁹⁢(97-digit number)
69665282763098028861…31887672154939164479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.966 Γ— 10⁹⁢(97-digit number)
69665282763098028861…31887672154939164481
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
1.393 Γ— 10⁹⁷(98-digit number)
13933056552619605772…63775344309878328959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.393 Γ— 10⁹⁷(98-digit number)
13933056552619605772…63775344309878328961
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
2.786 Γ— 10⁹⁷(98-digit number)
27866113105239211544…27550688619756657919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.786 Γ— 10⁹⁷(98-digit number)
27866113105239211544…27550688619756657921
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
5.573 Γ— 10⁹⁷(98-digit number)
55732226210478423089…55101377239513315839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.573 Γ— 10⁹⁷(98-digit number)
55732226210478423089…55101377239513315841
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:57,731,959 XPMΒ·at block #6,810,981 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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