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Block #976,988

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/16/2015, 11:56:43 AM Β· Difficulty 10.8478 Β· 5,829,201 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
89ca8b327e01035cfd0e00764ef87d1f3bbca5b9dbeeaea26ee8ddc8e693b93e
View on Chainz β†—

Height

#976,988

Difficulty

10.847790

Transactions

3

Size

1.37 KB

Version

2

Bits

0ad908bd

Nonce

151,328,239

Timestamp

3/16/2015, 11:56:43 AM

Confirmations

5,829,201

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7d2460a5bac84d36056e420aaabe9ce2aef7b1a2c5110031ffffab2481fd6c5e
Transactions (3)
Coinbase46f0b1a5c3a757…f86cf55f3958e1
1 in β†’ 1 out8.5000 XPM116 B
ANSXnLY2…Sd25TjkD
a562faf79d9e1c…8411c7913104b2
2 in β†’ 2 out15.8074 XPM375 B
AbenGgGQ…P3y2oSXwAMFwBo1q…R46NyNme
c74511439dc997…876e73fea126c5
5 in β†’ 2 out20.0242 XPM817 B
AWk6Trdx…Wg3ujSp5AKpWZZCf…r47GeyY1
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.

1.144 Γ— 10⁹⁷(98-digit number)
11440614123189000872…01059912809033086719
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
1.144 Γ— 10⁹⁷(98-digit number)
11440614123189000872…01059912809033086719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.144 Γ— 10⁹⁷(98-digit number)
11440614123189000872…01059912809033086721
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
2.288 Γ— 10⁹⁷(98-digit number)
22881228246378001744…02119825618066173439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.288 Γ— 10⁹⁷(98-digit number)
22881228246378001744…02119825618066173441
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
4.576 Γ— 10⁹⁷(98-digit number)
45762456492756003489…04239651236132346879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.576 Γ— 10⁹⁷(98-digit number)
45762456492756003489…04239651236132346881
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
9.152 Γ— 10⁹⁷(98-digit number)
91524912985512006979…08479302472264693759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.152 Γ— 10⁹⁷(98-digit number)
91524912985512006979…08479302472264693761
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
1.830 Γ— 10⁹⁸(99-digit number)
18304982597102401395…16958604944529387519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.830 Γ— 10⁹⁸(99-digit number)
18304982597102401395…16958604944529387521
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:57,693,598 XPMΒ·at block #6,806,188 Β· updates every 60s
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