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Block #1,982,270

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/13/2017, 10:06:33 PM Β· Difficulty 10.7534 Β· 4,844,638 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0919e4fdd405f93f0ffa9f3a91688a14286fa03f0661d1ae67fcb8a87896c584
View on Chainz β†—

Height

#1,982,270

Difficulty

10.753437

Transactions

2

Size

574 B

Version

2

Bits

0ac0e13e

Nonce

613,214,119

Timestamp

2/13/2017, 10:06:33 PM

Confirmations

4,844,638

Mined by

⛏️ P2SHAW1X3jua6ohyoayjEQuKrX6mQ7EiXrbNPt

Merkle Root

86b0782fd4bee04be7f1edac802128a9a7ae010db1e8a5005511b18a522d3544
Transactions (2)
Coinbase540216e6ff2246…b5daccb989e214
1 in β†’ 1 out8.6400 XPM109 B
AW1X3jua…EiXrbNPt
8736cfbadd864d…84ef78595c36d5
2 in β†’ 2 out0.2684 XPM374 B
ATPD4Y98…Uq2rGYW2ALrD53bo…v3pvJf75
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.

6.891 Γ— 10⁹⁢(97-digit number)
68918898784842488992…56243636977820016639
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
6.891 Γ— 10⁹⁢(97-digit number)
68918898784842488992…56243636977820016639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.891 Γ— 10⁹⁢(97-digit number)
68918898784842488992…56243636977820016641
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
1.378 Γ— 10⁹⁷(98-digit number)
13783779756968497798…12487273955640033279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.378 Γ— 10⁹⁷(98-digit number)
13783779756968497798…12487273955640033281
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
2.756 Γ— 10⁹⁷(98-digit number)
27567559513936995596…24974547911280066559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.756 Γ— 10⁹⁷(98-digit number)
27567559513936995596…24974547911280066561
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
5.513 Γ— 10⁹⁷(98-digit number)
55135119027873991193…49949095822560133119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.513 Γ— 10⁹⁷(98-digit number)
55135119027873991193…49949095822560133121
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
1.102 Γ— 10⁹⁸(99-digit number)
11027023805574798238…99898191645120266239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.102 Γ— 10⁹⁸(99-digit number)
11027023805574798238…99898191645120266241
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:57,859,432 XPMΒ·at block #6,826,907 Β· updates every 60s
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