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Block #907,018

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/23/2015, 7:38:50 PM Β· Difficulty 10.9352 Β· 5,905,700 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
68946f4c702e625c2405d0faf2621efccb0c907184945a6082a8d3426cccbdc0
View on Chainz β†—

Height

#907,018

Difficulty

10.935240

Transactions

2

Size

723 B

Version

2

Bits

0aef6be8

Nonce

435,042,549

Timestamp

1/23/2015, 7:38:50 PM

Confirmations

5,905,700

Mined by

⛏️ P2SHALKVEQmyoD7eKzCF6bkTkqXeSFb8gScWQt

Merkle Root

6cfc59d76c0703b6f38a82e6dd7554f13d546804ca679bfdab7c1c8c13c23452
Transactions (2)
Coinbase66bdcb7a2556ae…b881779ad1be59
1 in β†’ 1 out8.3600 XPM109 B
ALKVEQmy…b8gScWQt
3fad7da2865c83…79b746cb1757bd
3 in β†’ 2 out6.0001 XPM524 B
AY1We4vh…BefNQDuTAVpXLQz1…H7RDnPo3
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.

2.285 Γ— 10⁹⁴(95-digit number)
22859427555771157632…81793938306493683199
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
2.285 Γ— 10⁹⁴(95-digit number)
22859427555771157632…81793938306493683199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.285 Γ— 10⁹⁴(95-digit number)
22859427555771157632…81793938306493683201
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
4.571 Γ— 10⁹⁴(95-digit number)
45718855111542315265…63587876612987366399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.571 Γ— 10⁹⁴(95-digit number)
45718855111542315265…63587876612987366401
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
9.143 Γ— 10⁹⁴(95-digit number)
91437710223084630531…27175753225974732799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.143 Γ— 10⁹⁴(95-digit number)
91437710223084630531…27175753225974732801
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
1.828 Γ— 10⁹⁡(96-digit number)
18287542044616926106…54351506451949465599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.828 Γ— 10⁹⁡(96-digit number)
18287542044616926106…54351506451949465601
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
3.657 Γ— 10⁹⁡(96-digit number)
36575084089233852212…08703012903898931199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.657 Γ— 10⁹⁡(96-digit number)
36575084089233852212…08703012903898931201
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:57,745,782 XPMΒ·at block #6,812,717 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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