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Block #284,545

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 4:11:41 AM Β· Difficulty 9.9829 Β· 6,521,131 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6001ee71df52fcdf1132490dc146e9aec8f652520d4e68dc9174b8325ad003c1
View on Chainz β†—

Height

#284,545

Difficulty

9.982888

Transactions

2

Size

1.37 KB

Version

2

Bits

09fb9e8e

Nonce

27,679

Timestamp

11/30/2013, 4:11:41 AM

Confirmations

6,521,131

Mined by

⛏️ WaReAGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

8ee93a959ece9d194b10eeed24c1650649b7adee10594fcb52228628d80f943e
Transactions (2)
Coinbase5527e67ed6f3c8…41fa7640262637
1 in β†’ 31 out10.0000 XPM1.09 KB
AGFAJ5YL…ZEnBbk6GAQwRN8bE…V8PsTcY9AWZd1qVJ…9pj9yfPaAWQyM49v…zN9UeNMmAcs9SHrk…QJSB8SFG
cbf2cd0a5b8b57…48bd41841ab754
1 in β†’ 1 out3.0844 XPM192 B
AaB6Fg4D…Hdv4csPU
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.

1.075 Γ— 10⁹⁴(95-digit number)
10756108781780167003…03960808222110028799
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
1.075 Γ— 10⁹⁴(95-digit number)
10756108781780167003…03960808222110028799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.075 Γ— 10⁹⁴(95-digit number)
10756108781780167003…03960808222110028801
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
2.151 Γ— 10⁹⁴(95-digit number)
21512217563560334006…07921616444220057599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.151 Γ— 10⁹⁴(95-digit number)
21512217563560334006…07921616444220057601
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
4.302 Γ— 10⁹⁴(95-digit number)
43024435127120668012…15843232888440115199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.302 Γ— 10⁹⁴(95-digit number)
43024435127120668012…15843232888440115201
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
8.604 Γ— 10⁹⁴(95-digit number)
86048870254241336025…31686465776880230399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.604 Γ— 10⁹⁴(95-digit number)
86048870254241336025…31686465776880230401
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
1.720 Γ— 10⁹⁡(96-digit number)
17209774050848267205…63372931553760460799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.720 Γ— 10⁹⁡(96-digit number)
17209774050848267205…63372931553760460801
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:57,689,487 XPMΒ·at block #6,805,675 Β· updates every 60s
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