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Block #2,125,299

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/20/2017, 11:48:47 AM Β· Difficulty 10.9187 Β· 4,716,711 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
29a128227079b874c291e5c8c15bbcc525b1556f0b35fa0031e3826332f50877
View on Chainz β†—

Height

#2,125,299

Difficulty

10.918692

Transactions

1

Size

242 B

Version

2

Bits

0aeb2f5f

Nonce

689,182,505

Timestamp

5/20/2017, 11:48:47 AM

Confirmations

4,716,711

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

4cb033dac77f6ceaccfc47089050c8862c41f28f3bc19620d43777514b1d7eab
Transactions (1)
Coinbase4cb033dac77f6c…3777514b1d7eab
1 in β†’ 2 out8.3700 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…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.

2.833 Γ— 10⁹⁡(96-digit number)
28335109022710540747…17236859696105140719
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
2.833 Γ— 10⁹⁡(96-digit number)
28335109022710540747…17236859696105140719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.833 Γ— 10⁹⁡(96-digit number)
28335109022710540747…17236859696105140721
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
5.667 Γ— 10⁹⁡(96-digit number)
56670218045421081495…34473719392210281439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.667 Γ— 10⁹⁡(96-digit number)
56670218045421081495…34473719392210281441
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
1.133 Γ— 10⁹⁢(97-digit number)
11334043609084216299…68947438784420562879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.133 Γ— 10⁹⁢(97-digit number)
11334043609084216299…68947438784420562881
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
2.266 Γ— 10⁹⁢(97-digit number)
22668087218168432598…37894877568841125759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.266 Γ— 10⁹⁢(97-digit number)
22668087218168432598…37894877568841125761
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
4.533 Γ— 10⁹⁢(97-digit number)
45336174436336865196…75789755137682251519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.533 Γ— 10⁹⁢(97-digit number)
45336174436336865196…75789755137682251521
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
9.067 Γ— 10⁹⁢(97-digit number)
90672348872673730392…51579510275364503039
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
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