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Block #2,133,716

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 5:42:37 PM Β· Difficulty 10.9091 Β· 4,706,364 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
99924ad5aa155b79678a50b74e5611e59477bff7a268bb4897dcc4054f27f9a1
View on Chainz β†—

Height

#2,133,716

Difficulty

10.909077

Transactions

1

Size

199 B

Version

2

Bits

0ae8b943

Nonce

511,041,302

Timestamp

5/26/2017, 5:42:37 PM

Confirmations

4,706,364

Mined by

⛏️ P2SHAeGbGh2eRsHgTBuYDdbizJJwcM1LopREwr

Merkle Root

2c7892fb67bc0c3e3cd8eec8ec3648d08c377bcc9a6bbb25f5cae0b709a1ed0d
Transactions (1)
Coinbase2c7892fb67bc0c…cae0b709a1ed0d
1 in β†’ 1 out8.3900 XPM109 B
AeGbGh2e…1LopREwr
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.

3.006 Γ— 10⁹⁡(96-digit number)
30067940672627029142…38697483863595141759
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
3.006 Γ— 10⁹⁡(96-digit number)
30067940672627029142…38697483863595141759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.006 Γ— 10⁹⁡(96-digit number)
30067940672627029142…38697483863595141761
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
6.013 Γ— 10⁹⁡(96-digit number)
60135881345254058285…77394967727190283519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.013 Γ— 10⁹⁡(96-digit number)
60135881345254058285…77394967727190283521
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
1.202 Γ— 10⁹⁢(97-digit number)
12027176269050811657…54789935454380567039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.202 Γ— 10⁹⁢(97-digit number)
12027176269050811657…54789935454380567041
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
2.405 Γ— 10⁹⁢(97-digit number)
24054352538101623314…09579870908761134079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.405 Γ— 10⁹⁢(97-digit number)
24054352538101623314…09579870908761134081
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
4.810 Γ— 10⁹⁢(97-digit number)
48108705076203246628…19159741817522268159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.810 Γ— 10⁹⁢(97-digit number)
48108705076203246628…19159741817522268161
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
9.621 Γ— 10⁹⁢(97-digit number)
96217410152406493256…38319483635044536319
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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