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Block #2,133,281

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 9:48:26 AM Β· Difficulty 10.9098 Β· 4,706,501 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
edcb9e296bf479279bfed0921487a2c93bce70c61545241c26ac52f65798cf38
View on Chainz β†—

Height

#2,133,281

Difficulty

10.909795

Transactions

1

Size

201 B

Version

2

Bits

0ae8e859

Nonce

1,825,425,647

Timestamp

5/26/2017, 9:48:26 AM

Confirmations

4,706,501

Mined by

⛏️ P2SHAVhqKfhCmWRF7uyPDGLBGhxwr47YvA6mov

Merkle Root

cf9e3f807c42c552c5ec72bc02866eb04b42c742f39e44778c3a2a2a27755bb1
Transactions (1)
Coinbasecf9e3f807c42c5…3a2a2a27755bb1
1 in β†’ 1 out8.3900 XPM109 B
AVhqKfhC…7YvA6mov
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.

2.139 Γ— 10⁹⁸(99-digit number)
21390305451564263312…15761130536336752639
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
2.139 Γ— 10⁹⁸(99-digit number)
21390305451564263312…15761130536336752639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.139 Γ— 10⁹⁸(99-digit number)
21390305451564263312…15761130536336752641
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
4.278 Γ— 10⁹⁸(99-digit number)
42780610903128526624…31522261072673505279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.278 Γ— 10⁹⁸(99-digit number)
42780610903128526624…31522261072673505281
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
8.556 Γ— 10⁹⁸(99-digit number)
85561221806257053248…63044522145347010559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.556 Γ— 10⁹⁸(99-digit number)
85561221806257053248…63044522145347010561
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
1.711 Γ— 10⁹⁹(100-digit number)
17112244361251410649…26089044290694021119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.711 Γ— 10⁹⁹(100-digit number)
17112244361251410649…26089044290694021121
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
3.422 Γ— 10⁹⁹(100-digit number)
34224488722502821299…52178088581388042239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.422 Γ— 10⁹⁹(100-digit number)
34224488722502821299…52178088581388042241
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
6.844 Γ— 10⁹⁹(100-digit number)
68448977445005642598…04356177162776084479
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:57,962,546 XPMΒ·at block #6,839,781 Β· updates every 60s
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