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Block #363,232

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/17/2014, 7:07:44 AM Β· Difficulty 10.4116 Β· 6,439,931 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb2c4f7ae7380b7343616267b75fd5fdeeef7757c00b58b0a4f082e06a2a5574
View on Chainz β†—

Height

#363,232

Difficulty

10.411607

Transactions

2

Size

844 B

Version

2

Bits

0a695f17

Nonce

265,626

Timestamp

1/17/2014, 7:07:44 AM

Confirmations

6,439,931

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ada44d1513ee835f12dfa4e7ed417816b0eed4c2b7ed34383db994e9bb2ea454
Transactions (2)
Coinbase1839e9fc07ac8c…4a516100cce4e5
1 in β†’ 1 out9.2200 XPM116 B
AbwWkWZt…kawDhufa
65a5b82d2e4812…7e0ee0f530730f
4 in β†’ 1 out8.8700 XPM637 B
APhZbt91…ERWP9zpq
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.

1.919 Γ— 10⁹⁷(98-digit number)
19197507889028192254…42444652047765940479
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
1.919 Γ— 10⁹⁷(98-digit number)
19197507889028192254…42444652047765940479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.919 Γ— 10⁹⁷(98-digit number)
19197507889028192254…42444652047765940481
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
3.839 Γ— 10⁹⁷(98-digit number)
38395015778056384509…84889304095531880959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.839 Γ— 10⁹⁷(98-digit number)
38395015778056384509…84889304095531880961
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
7.679 Γ— 10⁹⁷(98-digit number)
76790031556112769019…69778608191063761919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.679 Γ— 10⁹⁷(98-digit number)
76790031556112769019…69778608191063761921
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
1.535 Γ— 10⁹⁸(99-digit number)
15358006311222553803…39557216382127523839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.535 Γ— 10⁹⁸(99-digit number)
15358006311222553803…39557216382127523841
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
3.071 Γ— 10⁹⁸(99-digit number)
30716012622445107607…79114432764255047679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.071 Γ— 10⁹⁸(99-digit number)
30716012622445107607…79114432764255047681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.143 Γ— 10⁹⁸(99-digit number)
61432025244890215215…58228865528510095359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,669,320 XPMΒ·at block #6,803,162 Β· updates every 60s
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