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Block #2,318,367

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/2/2017, 2:38:02 AM Β· Difficulty 10.9138 Β· 4,524,845 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7babc2064b691b81e221a618709600552014f65d91b6fbfbe6c7cce865846b8a
View on Chainz β†—

Height

#2,318,367

Difficulty

10.913793

Transactions

1

Size

243 B

Version

2

Bits

0ae9ee59

Nonce

896,712,897

Timestamp

10/2/2017, 2:38:02 AM

Confirmations

4,524,845

Mined by

⛏️ P2SHAY5YR3dJofqYoCTR4V3jMedx3QdsVboVgS

Merkle Root

702c03b84cdc75f401ebd8ec3c0f9e045d6717e5c9581d3bb85d34761fdd813b
Transactions (1)
Coinbase702c03b84cdc75…5d34761fdd813b
1 in β†’ 2 out8.3800 XPM152 B
AY5YR3dJ…dsVboVgSAXbk7f7A…Tx7JECPG
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.

1.161 Γ— 10⁹⁷(98-digit number)
11615095652410675100…15987479651572360319
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
1.161 Γ— 10⁹⁷(98-digit number)
11615095652410675100…15987479651572360319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.161 Γ— 10⁹⁷(98-digit number)
11615095652410675100…15987479651572360321
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
2.323 Γ— 10⁹⁷(98-digit number)
23230191304821350200…31974959303144720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.323 Γ— 10⁹⁷(98-digit number)
23230191304821350200…31974959303144720641
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
4.646 Γ— 10⁹⁷(98-digit number)
46460382609642700401…63949918606289441279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.646 Γ— 10⁹⁷(98-digit number)
46460382609642700401…63949918606289441281
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
9.292 Γ— 10⁹⁷(98-digit number)
92920765219285400803…27899837212578882559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.292 Γ— 10⁹⁷(98-digit number)
92920765219285400803…27899837212578882561
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
1.858 Γ— 10⁹⁸(99-digit number)
18584153043857080160…55799674425157765119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.858 Γ— 10⁹⁸(99-digit number)
18584153043857080160…55799674425157765121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.716 Γ— 10⁹⁸(99-digit number)
37168306087714160321…11599348850315530239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,990,069 XPMΒ·at block #6,843,211 Β· updates every 60s
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