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Block #2,117,122

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2017, 8:16:35 AM Β· Difficulty 10.9051 Β· 4,710,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ecc0b83c038dab6323166d961042f6cd2b173aee533bb3defd9db3897d95645e
View on Chainz β†—

Height

#2,117,122

Difficulty

10.905074

Transactions

2

Size

11.69 KB

Version

2

Bits

0ae7b2e8

Nonce

571,538,841

Timestamp

5/15/2017, 8:16:35 AM

Confirmations

4,710,111

Mined by

⛏️ P2SHAMqSwr76MnKPi8tymGfwkeMmmCxE3pq2hR

Merkle Root

a085620cc883af08333b1825164f62010c952a1922a67851f9499e93ef6893a5
Transactions (2)
Coinbase59d8950d942f5a…4cf263118c4bff
1 in β†’ 1 out8.5200 XPM109 B
AMqSwr76…xE3pq2hR
3fe54cffeabb51…5fb898a0cc4ec4
79 in β†’ 2 out880.0700 XPM11.50 KB
AZ3QSf7f…zd1mV8buAFshbVvJ…o6mu8ouB
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.

3.496 Γ— 10⁹⁴(95-digit number)
34969174617564999645…05798466504963592039
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
3.496 Γ— 10⁹⁴(95-digit number)
34969174617564999645…05798466504963592039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.496 Γ— 10⁹⁴(95-digit number)
34969174617564999645…05798466504963592041
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
6.993 Γ— 10⁹⁴(95-digit number)
69938349235129999291…11596933009927184079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.993 Γ— 10⁹⁴(95-digit number)
69938349235129999291…11596933009927184081
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
1.398 Γ— 10⁹⁡(96-digit number)
13987669847025999858…23193866019854368159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.398 Γ— 10⁹⁡(96-digit number)
13987669847025999858…23193866019854368161
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
2.797 Γ— 10⁹⁡(96-digit number)
27975339694051999716…46387732039708736319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.797 Γ— 10⁹⁡(96-digit number)
27975339694051999716…46387732039708736321
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
5.595 Γ— 10⁹⁡(96-digit number)
55950679388103999433…92775464079417472639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.595 Γ— 10⁹⁡(96-digit number)
55950679388103999433…92775464079417472641
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:57,861,964 XPMΒ·at block #6,827,232 Β· updates every 60s
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