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Block #2,045,982

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/31/2017, 2:10:07 AM Β· Difficulty 10.6838 Β· 4,785,062 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ff0150f2c62c0003dd1e3a69e62cbed8131c31ed4cd844dd102b37037e616933
View on Chainz β†—

Height

#2,045,982

Difficulty

10.683845

Transactions

1

Size

209 B

Version

2

Bits

0aaf1078

Nonce

196,666,534

Timestamp

3/31/2017, 2:10:07 AM

Confirmations

4,785,062

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

273269ded35cc8e6e46fe1bd46663db599ebfac970a11fdbcc9c6ace2164b3ff
Transactions (1)
Coinbase273269ded35cc8…9c6ace2164b3ff
1 in β†’ 1 out8.7500 XPM118 B
AM6GYpjw…aw86QDtR
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.

4.298 Γ— 10⁹⁷(98-digit number)
42986122593920682393…20326716434892011519
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
4.298 Γ— 10⁹⁷(98-digit number)
42986122593920682393…20326716434892011519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.298 Γ— 10⁹⁷(98-digit number)
42986122593920682393…20326716434892011521
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
8.597 Γ— 10⁹⁷(98-digit number)
85972245187841364786…40653432869784023039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.597 Γ— 10⁹⁷(98-digit number)
85972245187841364786…40653432869784023041
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
1.719 Γ— 10⁹⁸(99-digit number)
17194449037568272957…81306865739568046079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.719 Γ— 10⁹⁸(99-digit number)
17194449037568272957…81306865739568046081
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
3.438 Γ— 10⁹⁸(99-digit number)
34388898075136545914…62613731479136092159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.438 Γ— 10⁹⁸(99-digit number)
34388898075136545914…62613731479136092161
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
6.877 Γ— 10⁹⁸(99-digit number)
68777796150273091829…25227462958272184319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.877 Γ— 10⁹⁸(99-digit number)
68777796150273091829…25227462958272184321
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:57,892,489 XPMΒ·at block #6,831,043 Β· updates every 60s
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