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Block #2,149,714

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/7/2017, 6:04:36 AM Β· Difficulty 10.8984 Β· 4,683,925 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c90b1875fc30297755e67ee6bf7e52a0aabb1b88327e0a8b6675a6bf713a8823
View on Chainz β†—

Height

#2,149,714

Difficulty

10.898376

Transactions

1

Size

199 B

Version

2

Bits

0ae5fbfd

Nonce

542,605,556

Timestamp

6/7/2017, 6:04:36 AM

Confirmations

4,683,925

Mined by

⛏️ P2SHAeJU4gBJxBmewroYt83ViSwSwEcfiXwbAw

Merkle Root

5d831a046c4c728e4a8f8249c1e02d248411320f85ff4941d399cc8f73024ad7
Transactions (1)
Coinbase5d831a046c4c72…99cc8f73024ad7
1 in β†’ 1 out8.4100 XPM109 B
AeJU4gBJ…cfiXwbAw
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.

4.786 Γ— 10⁹³(94-digit number)
47863865949086818728…99969793586189413839
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
4.786 Γ— 10⁹³(94-digit number)
47863865949086818728…99969793586189413839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.786 Γ— 10⁹³(94-digit number)
47863865949086818728…99969793586189413841
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
9.572 Γ— 10⁹³(94-digit number)
95727731898173637456…99939587172378827679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.572 Γ— 10⁹³(94-digit number)
95727731898173637456…99939587172378827681
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
1.914 Γ— 10⁹⁴(95-digit number)
19145546379634727491…99879174344757655359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.914 Γ— 10⁹⁴(95-digit number)
19145546379634727491…99879174344757655361
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
3.829 Γ— 10⁹⁴(95-digit number)
38291092759269454982…99758348689515310719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.829 Γ— 10⁹⁴(95-digit number)
38291092759269454982…99758348689515310721
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
7.658 Γ— 10⁹⁴(95-digit number)
76582185518538909965…99516697379030621439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.658 Γ— 10⁹⁴(95-digit number)
76582185518538909965…99516697379030621441
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:57,913,324 XPMΒ·at block #6,833,638 Β· updates every 60s
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