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Block #1,681,710

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2016, 12:46:16 PM Β· Difficulty 10.7167 Β· 5,162,052 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fff48e7bc46ac663fe160756ce26d503c6fc9573dfa8d217ae6822c1f0fb837e
View on Chainz β†—

Height

#1,681,710

Difficulty

10.716695

Transactions

1

Size

198 B

Version

2

Bits

0ab7794b

Nonce

1,110,965,361

Timestamp

7/20/2016, 12:46:16 PM

Confirmations

5,162,052

Mined by

⛏️ P2SHAU89Nav2LcDXMcY5ktJY36BorLt5T4FqBQ

Merkle Root

15db374067d3989cf216f09a8f385a78d8635dfa1629e54ab14e214d583b7fd8
Transactions (1)
Coinbase15db374067d398…4e214d583b7fd8
1 in β†’ 1 out8.6900 XPM109 B
AU89Nav2…t5T4FqBQ
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.

1.170 Γ— 10⁹³(94-digit number)
11703147098350273960…01213672696057697039
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
1.170 Γ— 10⁹³(94-digit number)
11703147098350273960…01213672696057697039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.170 Γ— 10⁹³(94-digit number)
11703147098350273960…01213672696057697041
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
2.340 Γ— 10⁹³(94-digit number)
23406294196700547920…02427345392115394079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.340 Γ— 10⁹³(94-digit number)
23406294196700547920…02427345392115394081
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
4.681 Γ— 10⁹³(94-digit number)
46812588393401095840…04854690784230788159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.681 Γ— 10⁹³(94-digit number)
46812588393401095840…04854690784230788161
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
9.362 Γ— 10⁹³(94-digit number)
93625176786802191681…09709381568461576319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.362 Γ— 10⁹³(94-digit number)
93625176786802191681…09709381568461576321
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
1.872 Γ— 10⁹⁴(95-digit number)
18725035357360438336…19418763136923152639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.872 Γ— 10⁹⁴(95-digit number)
18725035357360438336…19418763136923152641
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
3.745 Γ— 10⁹⁴(95-digit number)
37450070714720876672…38837526273846305279
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:57,994,469 XPMΒ·at block #6,843,761 Β· updates every 60s
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