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Block #1,949,786

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/22/2017, 5:34:31 PM Β· Difficulty 10.7247 Β· 4,858,274 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e3cb6c2075cbd55250dfa05a246e3e200cf2620ac43058eb14d7120dd8c1eadf
View on Chainz β†—

Height

#1,949,786

Difficulty

10.724680

Transactions

1

Size

201 B

Version

2

Bits

0ab98499

Nonce

11,309

Timestamp

1/22/2017, 5:34:31 PM

Confirmations

4,858,274

Mined by

⛏️ P2SHAdR3SMVt6VHfdqBhG6aGDPFuE82zrhAR7g

Merkle Root

7bd12cb55b0c7c9799eaa2d91c611dd7f715a300b57543bfe0ed8198ad38c101
Transactions (1)
Coinbase7bd12cb55b0c7c…ed8198ad38c101
1 in β†’ 1 out8.6800 XPM109 B
AdR3SMVt…2zrhAR7g
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.

2.466 Γ— 10¹⁰⁰(101-digit number)
24664800149146611887…48130910394144120399
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
2.466 Γ— 10¹⁰⁰(101-digit number)
24664800149146611887…48130910394144120399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.466 Γ— 10¹⁰⁰(101-digit number)
24664800149146611887…48130910394144120401
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
4.932 Γ— 10¹⁰⁰(101-digit number)
49329600298293223775…96261820788288240799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.932 Γ— 10¹⁰⁰(101-digit number)
49329600298293223775…96261820788288240801
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
9.865 Γ— 10¹⁰⁰(101-digit number)
98659200596586447551…92523641576576481599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.865 Γ— 10¹⁰⁰(101-digit number)
98659200596586447551…92523641576576481601
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
1.973 Γ— 10¹⁰¹(102-digit number)
19731840119317289510…85047283153152963199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.973 Γ— 10¹⁰¹(102-digit number)
19731840119317289510…85047283153152963201
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
3.946 Γ— 10¹⁰¹(102-digit number)
39463680238634579020…70094566306305926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.946 Γ— 10¹⁰¹(102-digit number)
39463680238634579020…70094566306305926401
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:57,708,524 XPMΒ·at block #6,808,059 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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