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Block #960,406

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/3/2015, 10:55:16 PM Β· Difficulty 10.8860 Β· 5,848,358 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d589f895cbfc2cb6df3a619837e95127b27f8a790249be5c0106a57daf6115ce
View on Chainz β†—

Height

#960,406

Difficulty

10.886020

Transactions

2

Size

582 B

Version

2

Bits

0ae2d22f

Nonce

106,705,708

Timestamp

3/3/2015, 10:55:16 PM

Confirmations

5,848,358

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7fdd8c89d070c0ae6ef32d71a96ee655c3439839f3a4fb44a3802a3d05505c46
Transactions (2)
Coinbase93ef4786633550…9030a3cf45f929
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
1d460726249b72…ce57d94b38d2b5
2 in β†’ 2 out1.1476 XPM375 B
AP4BUBdX…xZ92AHh8AMZc21EG…45KXiN7h
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.

9.934 Γ— 10⁹⁷(98-digit number)
99348519512701452773…29427205064916441599
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
9.934 Γ— 10⁹⁷(98-digit number)
99348519512701452773…29427205064916441599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.934 Γ— 10⁹⁷(98-digit number)
99348519512701452773…29427205064916441601
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
1.986 Γ— 10⁹⁸(99-digit number)
19869703902540290554…58854410129832883199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.986 Γ— 10⁹⁸(99-digit number)
19869703902540290554…58854410129832883201
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
3.973 Γ— 10⁹⁸(99-digit number)
39739407805080581109…17708820259665766399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.973 Γ— 10⁹⁸(99-digit number)
39739407805080581109…17708820259665766401
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
7.947 Γ— 10⁹⁸(99-digit number)
79478815610161162218…35417640519331532799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.947 Γ— 10⁹⁸(99-digit number)
79478815610161162218…35417640519331532801
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
1.589 Γ— 10⁹⁹(100-digit number)
15895763122032232443…70835281038663065599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.589 Γ— 10⁹⁹(100-digit number)
15895763122032232443…70835281038663065601
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
3.179 Γ— 10⁹⁹(100-digit number)
31791526244064464887…41670562077326131199
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:57,714,160 XPMΒ·at block #6,808,763 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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