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Block #122,662

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2013, 3:13:11 PM Β· Difficulty 9.7564 Β· 6,690,061 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2ee816b9db7845b72fd632f3c8236b587ce9fef329d4698eb1a74c213cd72b4d
View on Chainz β†—

Height

#122,662

Difficulty

9.756430

Transactions

1

Size

200 B

Version

2

Bits

09c1a56d

Nonce

282,535

Timestamp

8/18/2013, 3:13:11 PM

Confirmations

6,690,061

Mined by

⛏️ P2SHAGxV11XYRn17tdWsAaq1cqMu2qjqRvF7Au

Merkle Root

c89b9254930acf6dbae4d046e98a46a9c448367cc53e0bb6f3cde32c1747192f
Transactions (1)
Coinbasec89b9254930acf…cde32c1747192f
1 in β†’ 1 out10.4900 XPM109 B
AGxV11XY…jqRvF7Au
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.

8.301 Γ— 10⁹⁢(97-digit number)
83014700494903760534…98422355858538354669
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
8.301 Γ— 10⁹⁢(97-digit number)
83014700494903760534…98422355858538354669
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.301 Γ— 10⁹⁢(97-digit number)
83014700494903760534…98422355858538354671
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
1.660 Γ— 10⁹⁷(98-digit number)
16602940098980752106…96844711717076709339
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.660 Γ— 10⁹⁷(98-digit number)
16602940098980752106…96844711717076709341
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
3.320 Γ— 10⁹⁷(98-digit number)
33205880197961504213…93689423434153418679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.320 Γ— 10⁹⁷(98-digit number)
33205880197961504213…93689423434153418681
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
6.641 Γ— 10⁹⁷(98-digit number)
66411760395923008427…87378846868306837359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.641 Γ— 10⁹⁷(98-digit number)
66411760395923008427…87378846868306837361
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
1.328 Γ— 10⁹⁸(99-digit number)
13282352079184601685…74757693736613674719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.328 Γ— 10⁹⁸(99-digit number)
13282352079184601685…74757693736613674721
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:57,745,823 XPMΒ·at block #6,812,722 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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